Designing SamplesSection 5.1 Continued

Sample Designs

A simple random sample (SRS) of size n contains n individuals from the population chosen so that every set of n individuals has an equal chance of being selected.

Sample Designs

Example: SRS or not? I want a sample of nine students from

the class, so I put each of your names in a hat and draw out nine of them. ▪ Does each individual have an equal chance of

being chosen? ▪ Does each group of nine people have an

equal chance of being chosen?

Sample Designs

Example: SRS or not? I want a sample of nine students from

the class but I know that there are three juniors and 17 seniors in class, so I pick one junior at random and eight seniors. ▪ Does each individual have an equal chance of

being chosen? ▪ Does each group of nine people have an

equal chance of being chosen?

Sample Designs

Better than a hat: computers. Software can choose an SRS from a list

of the individuals in a list.Not quite as easy as software, but

still better than a hat: a table of random digits

Sample Designs

A table of random digits is a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with two properties: Each entry in the table is equally likely to

be any of the ten digits 0 through 9. The entries are independent of each other.

(Knowing one part of the table tells you nothing about the rest of the table.)

Sample Designs

Table B in the back of your book.

Sample Designs

Each entry is equally likely to be 0 – 9.

Each pair of entries is equally likely to be 00 – 99.

Each triple of entries is equally likely to be 000 – 999.

And so on…

Sample Designs

Example: Using a random digit table.

Read on page 276 the example 5.4

Sample Designs

A stratified random sample first divides a population into groups of similar individuals called strata. Then separate SRS’s are chosen from each group (stratum) and combined to make the full sample.

Sample Designs

Practice problems: 7-12 (p. 274 & 279)

Cautions about samples

Choosing samples randomly eliminates human bias from the choice of sample, but… What problems might remain?

Brainstorm.

Cautions about samples

Undercoverage Having an inaccurate list of the

population▪ Ex: Who is excluded from a survey of

“households”? ▪ Who is excluded from a telephone survey?

Cautions about samples

Nonresponse Occurs when selected individuals cannot

be contacted or refuse to cooperate

Examples

Which problem (undercoverage or nonresponse) is represented? It is impossible to keep a perfectly

complete list of addresses for the U.S. Census

Homeless people do not have addresses In 1990, 35% of people who were mailed

Census forms did not return them.

Response Bias

Results may be influenced by behavior of either the interviewer or the respondent

Response Bias

How might response bias show up in these situations? A survey about drug use or other illegal

behavior Questions asking people to recall events,

like: “Have you visited the dentist in the last six months?”

Response Bias

The wording of questions can often lead to bias “It is estimated that disposable diapers

account for less than 2% of the trash in today’s landfills. In contrast, beverage containers, third-class mail, and yard wastes are estimated to account for 21% of the trash in landfills. Given this, in your opinion, would it be fair to ban disposable diapers?”

Response Bias

“Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?”

“Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened?”

Response Bias

“Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?” 22% said possible

“Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened?” 1% said possible

Inference about the population

Even if we can eliminate most of the bias in a sample, the results from the sample are rarely exactly the same as for the population Each different sample pulls different

individuals, so results will vary from sample to sample

Results are rarely correct for the population

Inference about the population

Since we use random sampling, we can use the laws of probability (later chapters!) We’ll be able to figure out the margin of

error (also in later chapters)

Inference about the population

Just know now: larger random samples give more accurate results than smaller samples.